calculus – if $u = arccos (frac{x+y}{sqrt{x}+sqrt{y}})$ then $xfrac{partial u}{partial x} + yfrac{partial u}{partial y}$

Edit: this is a repost
Context: i’ve looked at PYQ’s and this year mock tests and found out that this question was one of the most repeated ones and i’m having an exam next week and my teachers are not available

The answer i got
$xfrac{partial u}{partial x} + yfrac{partial u}{partial y} = frac{-x(sqrt{x}+sqrt{y}-(x+y)frac{1}{2sqrt{x}})} {sin^2(u)(sqrt{x}+sqrt{y})^2}- frac{y(sqrt{x}+sqrt{y}-(x+y)frac{1}{2sqrt{y}}) } {sin^2(u)(sqrt{x}+sqrt{y})^2}$

The answer im getting is nowhere near the options that have been given

Options

1.$frac{-1}{2}sin(u)$

2. $frac{-1}{2}cot(u)$

3. $frac{-1}{2}tan(u)$

4. $frac{-1}{2}cos(u)$